Cohomology of Quaternionic Foliations and Orbifolds

TL;DR

This paper extends classical results on quaternionic K{"a}hler manifolds to foliations and orbifolds, establishing cohomological properties for transversely quaternionic structures and their leaf spaces.

Contribution

It introduces a framework for quaternionic K{"a}hler foliations and generalizes cohomology results to quaternionic orbifolds, linking foliation theory with quaternionic geometry.

Findings

Foliated versions of Kraines and Fujiki results established

Cohomology of quaternionic orbifolds characterized

Connections between foliations and orbifold structures demonstrated

Abstract

Starting with a concise review of quaternionic geometry and quaternionic K{\"a}hler manifolds, we define a transversely quaternionic K{\"a}hler foliation. Then we formulate and prove the foliated versions of the now classical results of V.Y. Kraines and A. Fujiki on the cohomology of quaternionic K{\"a}hler manifolds. Finally, as any orbifold can be realized as the leaf space of a suitably defined Riemannian foliation we reformulate our results for quaternionic orbifolds.